Orbital frustration at the origin of the magnetic behavior in LiNiO2

We report on the ESR, magnetization, and magnetic susceptibility measurements performed over a large temperature range, from 1.5 to 750 K, on high-quality stoichiometric LiNiO2. We find that this compound displays two distinct temperature regions where its magnetic behavior is anomalous. With the help of a statistical model based on the Kugel'-Khomskii Hamiltonian, we show that below T(of) approximately 400 K, an orbitally frustrated state characteristic of the triangular lattice is established. This then gives a solution to the long-standing controversial problem of the magnetic behavior in LiNiO2.     

Phenylacetylene as a new surrogate standard for the determination of BTEX by GC/FID

Benzene, toluene, ethylbenzene, xylene (short form: BTEX) and other monoaromatic compounds are environmental contaminants which are often analyzed by GC/FID. For the calculation of BTEX concentrations in water samples normally external quantification with defined BTEX solutions is sufficient. However, for accurate quantification of BTEX in complex matrices it is necessary to use internal standards, e.g. 1-chlorohexane. Isotopes of BTEX are usually the best alternative but they are only applicable to GC/MS, because their retention times are similar to the original BTEX. 1-Chlorohexane and phenylacetylene were compared with respect to their quality as internal standards. Good results were obtained with the monoaromatic phenylacetylene as a surrogate standard. The physical properties of phenylacetylene are very similar to BTEX species and it normally does not occur in environmental samples. 1-Chlorohexane was more strongly adsorbed on the used soil than BTEX during sample preparation. This fact suggests that the single aromatic rings of BTEX and phenylacetylene are mainly responsible for the adsorption behavior.     

Asymptotic Cones of Finitely Generated Groups

Answering a question of Gromov [7], we shall present an exampleof a finitely generated group and two non-principal ultrafiltersA, B such that the asymptotic cones Con_A and Con_B are nothomeomorphic. 1991 Mathematics Subject Classification 20F06,20F32.     

Local Rules and Fitness Landscapes: A Catastrophe Model

This paper examines the imposition of local rules in five mail delivery centres of Australia Post. Local rules are patterns of behaviour used by subunits of an organization to optimise their payoff. These local rules may ultimately benefit the total organization. Fitness landscapes are used to examine the emergence of local rules in this workplace. This research examined the relationship between the time taken to sort the mail and the volume of this mail. Work rates show a clear catastrophe shift; that is, work rates suddenly drop when the volume of mail exceeds a certain level, as Postal Delivery Officers apply local rules to maximise gains inherent in the pay structures. Such behaviour is close to that predicted by Kauffman (1995) in computer simulations of lattices and may be indicative of the application of local rules in organizations. The implications of the use of local rules are that behaviour in social systems may be dictated by systemic and emergent processes which are outside immediate management control. A further implication is that organizations may be structured to a significant extent by such local rules.     

Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty

A dynamic (multi-stage) stochastic programming model for the weekly cost-optimal generation of electric power in a hydro-thermal generation system under uncertain demand (or load) is developed. The model involves a large number of mixed-integer (stochastic) decision variables and constraints linking time periods and operating power units. A stochastic Lagrangian relaxation scheme is designed by assigning (stochastic) multipliers to all constraints coupling power units. It is assumed that the stochastic load process is given (or approximated) by a finite number of realizations (scenarios) in scenario tree form. Solving the dual by a bundle subgradient method leads to a successive decomposition into stochastic single (thermal or hydro) unit subproblems. The stochastic thermal and hydro subproblems are solved by a stochastic dynamic programming technique and by a specific descent algorithm, respectively. A Lagrangian heuristics that provides approximate solutions for the first stage (primal) decisions starting from the optimal (stochastic) multipliers is developed. Numerical results are presented for realistic data from a German power utility and for numbers of scenarios ranging from 5 to 100 and a time horizon of 168 hours. The sizes of the corresponding optimization problems go up to 200000 binary and 350000 continuous variables, and more than 500000 constraints.     

Reconstruction of the Wigner transform of a rotationally symmetric two-dimensional beam from the Wigner transform of the beam's one-dimensional sample

A coherent rotationally symmetric two-dimensional beam is essentially one-dimensional in content: It is fully determined by the one-dimensional sample along a diagonal of the circularly symmetric field distribution in a transverse plane. The linear transform that reconstructs the four-dimensional Wigner distribution of the full two-dimensional beam from the two-dimensional Wigner distribution of the one-dimensional sample is presented.     

Waves and rays in uniaxial birefringent crystals

In this paper, we present a more elaborate and complete way of the formalism that we have developed in successive steps for ray tracing through uniaxial birefringent media in view of the optical design. With the obtained formulas we analyze in detail what we see through a cleavage calcite crystal.